A senior United States official says progress has been made in two days of U.S.-Russian talks about ways to cut nuclear weapons. The U.S. official says he expects a final deal in time for the May summit between President Bush and Russian President Vladimir Putin.

U.S. Undersecretary of State John Bolton says the United States and Russia have reaffirmed their intention to make significant cuts in their nuclear arsenals.

Mr. Bolton says the United States is prepared to slash strategic weapons by two-thirds, from 6,000 to between 1,700 and 2,200. He says Russia might go as low as 1,500. But, he says, differences still remain over the precise method of counting missiles to be cut, and whether they should be destroyed or stored.

"The precedent in prior arms control agreements, of course, is that the treaties have not made any mention of what happens to warheads that are downloaded," he said. "Some go into storage, some are dismantled, some are used for other purposes. I think the parties have reached an understanding that, in order to reach an agreement by the summit in May, we have to focus on the subject that is of most concern to us, and that is to say the operationally deployed warheads."

Mr. Bolton says the United States wants only so-called operationally deployed warheads to be counted in the missile reductions. These are warheads that are actually mounted on delivery systems, ready to be fired. He says Russia wants the cuts to include both targeted warheads and missile delivery systems.

Mr. Bolton says the two nations also have not yet agreed on measures to verify the other country's nuclear warhead cuts. And, he says, the United States has included a withdrawal clause in the draft agreement.

"We had also proposed to the Russians that, short of actual withdrawal, there might be a mechanism whereby we could give notice, if we felt international geostrategic circumstances had changed to a point where the offensive nuclear weapons range might be adjusted," he said. "So, we could adjust to that range, without actually withdrawing from the treaty. We have had some interesting discussions on that. I think it would be fair to say that we have not reached agreement."

Mr. Bolton calls this round of talks very productive, and says he and Russian negotiator Gregory Mamedov will hold a fourth negotiating round in Moscow in a month.